Angular resolution limit of two closely-spaced point sources based on information theoretic criteria

The statistical angular resolution limit (RL) of two closely-spaced point sources in array processing is analyzed based on the framework of hypothesis test. For the first time, the general case where neither the source signals nor the parameters of interest are known under both the null hypothesis and the alternative is considered. Using the theory of misspecified model, the asymptotic distribution of the twice log-generalized-likelihood-ratio statistic under the alternative hypothesis is derived. It is shown to be non-central chi-squared distributed with degrees of freedom equal to the difference in dimensionality of the parameters under both hypotheses, and non-centrality parameter closely related to the Kullback-Leibler divergence of the probability density functions under both hypotheses. The information-theoretic-criteria-based model order selection rules are adopted and a novel detection-based RL is derived. The Cramér-Rao bound (CRB)-based RL is also derived for comparison. It is observed that the detection-based RL and the CRB-based RL are fundamentally different in such general case. Numerical simulations verify the theoretical results.